Equivalent Circuit Model of High Power LEDs forVLC Systems

Xicong Li1, Zabih Ghassemlooy1, Stanislav Zvanovec2, Min Zhang3, Andrew Burton1

1Optical Communications Research Group, Northumbria University, Newcastle upon Tyne, UK2Czech Technical University in Prague, Prague, Czech Republic

3Beijing University of Posts and Telecommunications, Beijing, China1xicong.li, z.ghassemlooy, andrew2.burton@northubria.ac.uk, 2xzvanove@fel.cvut.cz, 3mzhang@bupt.edu.cn

Abstract—The equivalent circuit model for two commercialhigh power LEDs for illuminance is proposed and extensivemeasurements have been carried out to verify the accuracy ofthe model. In addition, the frequency response of two LEDs inthe optical domain can be estimated using the transfer functionof electrical equivalent circuit. It is shown that, the electricalparasitics in the chip and packaging introduce significant at-tenuation beyond a resonance frequcency. Care should be takenwhen designing high-speed driver and/or equalization circuits forVLC systems.

Index Terms—LED, equivalent circuit, impedance, impedancematching, driver circuit, bandwidth, carrier lifetime, VLC

I. INTRODUCTION

Light emitting diodes (LEDs) have been intensively inves-tigated since Burrus [1] fabricated the first LED for opticalfiber communication systems. LEDs with high luminous andenergy efficiencies compared to traditional light sources ofincandescence and fluorescence, color rendering, reduced sizeand lower cost are currently being adopted in a wide range ofapplications. In addition, LEDs (i) light output can be changedor dimmed by simply adjusting the drive current up to the ratedmaximum level; and (ii) offer longer life span. LEDs can havevastly different characteristics with regard to, for example, thefrequency response (i.e., switching speed), luminous, colourrendering and efficiency. As for the LED’s frequency response,it is well known that its frequency response follows thefirst order system [2]–[5], whereby its modulation bandwidthis mainly limited by the effective carrier lifetime which istypically 2-5 ns for InGaAsP LEDs [6] with a correspondingbandwidth up to hundreds of MHz.

In recent years, we have seen a growing research interestin the emerging wireless technology of visible light com-munications (VLC), which uses both solid state and organicLEDs at the transmitter [7], [8]. VLC offers illumination, datacommunication, indoor localization and sensing. However,LEDs used for illuminance tend to have large areas (i.e., highcapacitance) and operate at high drive current, thus imposinga modulation bandwidth limit and driving complexity. Onthe other hand, LEDs for data communications should besmall in size with low capacitance and much reduced parasiticelements. Research on white LEDs for VLC systems hasmainly focused on algorithms, system implementation andperformance evaluation. However, not much has been reported

on the frequency response of LED devices within the contextof VLC systems.

The equivalent circuit model of the LED is of practicalimportance for designing efficient driver and/or modulationcircuits as well as equalizers to extend modulation bandwidth.The one port reflection measurement is an efficient approachbased on the S11 parameter to characterize the impedance andcarrier lifetime of lasers and LEDs [9]–[13]. In [14], [15], thismethod was adopted to characterize the equivalent circuit ofAlGaN based multiple quantum well (MQW) deep ultraviolet(UV) and double heterojunction (DH) LEDs. However, there islimited information in the literature on the equivalent circuitcharacterization of high-power LEDs used in VLC systems.Note that, here generally high-power LEDs refer to those witha single chip size not less than 1mm2 with a drive current of atleast 350 mA [16]–[18]. In this paper we investigate the effectsof parasitic elements on modulation bandwidth in high-powerLEDs within the context of VLC.

The rest of the paper is organized as following. The equiv-alent circuit model is given in Section II and measured resultsare shown in Section III as well as fitted element values.

II. SMALL SIGNAL MODEL

A. Theory

A practical LED chip can be modelled as a parallel RCcircuit [5, 6, 20, 21]. The resistance can be obtained fromthe differential resistance rd of LED’s intrinsic p-n junction,while the capacitance consists of the space-charge capacitanceCsc, which results in the delay of carrier injection to the p-njunction, and the diffusion capacitance Cd. The ultimate limitof LED modulation bandwidth is determined by the carrierrecombination lifetime τ = rdCd . Due to the parasitic Csc,the frequency response of the LED is given by:

H(w) =1

1 + jωτeff(1)

where τeff = rd(Cd + Csc) is the effective carrier lifetime,ω is the angular frequency, and j =

√−1.

In addition, real LED chips have a series resistance dueto current crowding under electrodes, ohmic contacts andbonding wires from the die [19]. Large size LEDs, especiallyhigh-power LEDs used in VLC systems, tend to have a largeCsc between the layers and a parasitic capacitance Ce between

electrodes as shown in Fig. 1 (note, Ce depends on the LEDchip design).

Fig. 1. A conventional LED: (a) Chip structure, and (b) A Red LED (fromCree XPE®)

B. PackagingFor high-power LEDs with large areas, packaging is im-

portant to ensure good heat dissipation and therefore longerlifetime. Commercial high power LED chips are availablein mainly three packages of conventional package, flip-chippackage and vertical package [16]. A red and a white LEDare considered in this paper. The red LED (Cree XPERED-L1-0000-00501) with the conventional chip package and rect-angular electrodes is shown in Fig. 1(b), while the whiteLED (Lumileds Luxeon Rebel LXML-PWC2) has a flip-chippackage with the phosphor coated on the GaN blue LED chip.External packages for the chips are availble in a wide varietyof ways. Both devices considered here are based on chip-on-ceramic board packaging in order to minimize the physicalsize [17].

An electrostatic discharge (ESD) protection diode (e.g.,Zener diodes) is another important component in LED pack-aging to protect the chip from damage. It comes in differentcombination with different parasitic [19]. The ESD parasiticcapacitance is included within the total bonding capacitanceCb together with the electrode capacitance Ce. Note that herethe ESD is modelled as a single capacitance for simplicity andits accurate model cannot be obtained due to its integration inthe package. Common ESD diodes will have a capacitanceof 500 pF to 10 nF with a zero bias, which can contributeto the distortion of high-speed signals beyond the operatingfrequency of 500MHz.

C. Equivalent Circuit ModelThe equivalent circuit for high power LEDs is shown in Fig.

2. The intrinsic LED model is composed of the differentialresistance rd and the junction capacitance Cj , which is thesum of the space-charge capacitance Csc and the diffusioncapacitance Cd . The parasitic consists of the series resistanceRs inside the LED chip, the series bonding resistance Rb,the series bonding inductance Lb and the parallel bondingcapacitance Cb . Note that Rg is the impedance of the source(50Ω for the vector network analyzer, VNA).

The impedance of an LED is given by:

ZLED = Rb + jωLb +1

jωCb//

(Rs +

1

jωCj//rd

)(2)

Fig. 2. The equivalent circuit model for the AC small signal.

where Cj = Csc + Cd is the junction capacitance.

D. Modulation Characteristics

The optical output can be obtained from (2) based onthe fact that optical power is proportional to the current ithrough the differential resistance, which is representative ofeffective modulated current through the active region. Theoutput voltage Vo = hird in Fig. 2 can be considered as thesmall-signal light output intensity of the LED [3], [10], whereh is the gain coefficient. Therefore, the frequency responseof the LED (including packaging) can be modelled using thevoltage transfer function as given by:

HLED(s) =Vo(s)

Vs(s)= h

rdZLED +Rg

= 1/

(s3RsLbCjCb

+ s2[Rb +Rg +RsCjCb + Lb

(Cb

Rs + rdrd

+ Cj

)]+ s

[Rb +Rg +

(Cb

Rs + rdrd

+ Cj

)+

Lb

rd+RsCj

]+

rd +Rb +Rg +Rs

rd

)(3)

where s = jω is the complex variable.To verify the validity of this method, the S21 parameter was

measured and compared with estimated response as presentedin the section III. It is interesting to notice that the LED’sresponse follows the first-order RC system at low frequencies,and attenuates significantly as a three-order system abovethe resonance peak caused by parasitic elements. From thestandpoint of driver or equalizer design, more gain should beprovided to compensate for the parasitic introduced attenua-tion.

III. MEASUREMENT SETUP AND RESULTS

The experimental measurement testbed is shown in Fig.3, which is composed of a VNA (Keysight E5061B, 5Hz-3GHz), a wide-band test fixture (Keysight 16197A, 3GHz)specifically designed for surface mounted components, a high-speed optical receiver (Newport Model-1601, 1GHz), a multi-mode optical fibre. All the measurements were carried out

at a room temperature of 20 C. The LEDs mounted on thetest fixture were driven using the reflection port of the vectornetwork analyser with a 50Ω output impedance, whereas thetransmission port of VNA was used to monitor the outputof the optical receiver. A short length multi-mode fibre wasused to connect LED and the optical receiver. The VNAwas calibrated prior to carrying out measurements. For eachLED we carried out measurements for the impedance and S21parameter for a range of bias voltage.

Fig. 3. Experimental setup

A. V-I Measurement

Using a source meter (Keithley 2400), we measured the V-Icurves for both LEDs as shown in Fig. 4. With the measureddata, we carried out curve fitting using the p-n junction diodeequation I = ISe

q(V−IRSDC)/nkT with a parasitic series

resistance RsDC, where IS is the reverse saturation current,

n is the ideal factor, k is the Boltzman constant, T is theabsolute temperature, q is the charge of an electron. Table Ilists fitted parameters for two devices.

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Voltage(V)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Cur

rent

(A)

White measuredWhite fittedRed measuredRed fitted

Fig. 4. Measured and fitted V-I curves of LEDs

TABLE IPARAMETERS FITTED

Description White LED Red LED

Reverse saturation current IS 1.13× 10−35 A 3.12× 10−21 A

Ideal factor n 1.34 1.98

Series resistance RsDC 0.015Ω 0.360Ω

B. Impedance Measurement

In order to ensure that LEDs are operating within the linearregion, an AC signal with an output power of −40 dBm wasused to measure the impedance for a range of bias voltagegenerated from the internal bias tee of the VNA’s reflectionport. The voltage across the LED was measured using a DCvoltage meter in order to estimate the bias current with the helpof V-I curves. Due to the high impedance of the voltage meter,the measured voltage can be used as an accurate estimateof voltage cross the LED. After measuring the DC voltage,the voltage meter was removed to eliminate its effect on themeasurement results. The impedance results were capturedfrom the VNA.

Figs. 5 and 6 show the measured impedance (only themagnitude vs the frequency is given here for clarity) of thewhite and red LEDs for a range of bias conditions. Tables IIand III list the estimated values of the elements. To illustratethe fitting method and its accuracy, the impedance of the redLED biased at (1.7V, 1.662V, 4.0mA), which representsthe DC bias voltage of VNA, voltage across the LED andestimated current, respectively, is shown in Fig. 7. The LEDbehaves like a low pass filter in the low frequency range (seethe inset at the left), and the first impedance floor can beestimated by Rb +Rs + rd. With the frequency increasing, asecond floor appears where Rd is shorted by Cj , thus makingthe corresponding value suitable to account for Rb + Rs

and the roll-off of the impedance to estimate Cj . Thelowest impedance dip is used to estimate Rb at the resonancefrequency of (2π

√LbCb)

−1provided the following condition

holds: ∣∣∣∣ 1

jωCb

∣∣∣∣≪ ∣∣∣∣Rs +1

jω(Csc + Cd)//rd

∣∣∣∣ (4)

At frequencies above the resonance peak, the impedance canbe used to estimate Lb since the parasitic inductance Lb isdominant (see the inset at the right). However, if (4) is notmet, then there will be inaccuracy in the estimation.

It has been observed that, the differential resistance estimat-ed using RSDC +nkT/qI0 (I0 is the bias current) accounts forrd in the model as well as Rsum = Rb+Rs+rd. This is evidentfrom Tables II and III, and can be explained by the measuredV-I curves, which can interpreted as the characteristics of theentire LED. Another observation is that, Rs decreases as thebias current increases, which is different from those lasers andLEDs used in communication systems [15], [20].

(1.7V, 1.662V, 4.0mA) is like (x,y,z) for bias voltages and current,see fig5,6. So I didn't add "and" here.

TABLE IIPARAMETERS FITTED FOR THE WHITE LED

Bias(V,mA) Rb(Ω) Cb(nF) Lb(nH) Rs(Ω) rd(Ω) Cj (nF) Rsum(Ω) nkT/qI0 +RsDC (Ω)

(0.000, 0) 0.20 3.36 2.45 − − − − −

(1.000, 0) 0.20 3.65 2.45 − − − − −

(2.000, 0) 0.20 4.19 2.45 − − − − −

(2.100, 0) 0.20 4.45 2.45 − − − − −

(2.200, 0) 0.20 4.99 2.45 − − − − −

(2.300, 0) 0.20 6.17 2.45 − − − − −

(2.400, 0) 0.20 8.16 2.45 − − − − −

(2.493, 0.2) 0.20 10.5 2.45 55.52 206.28 0.1 261.2 286.5

(2.558, 0.8) 0.20 12.2 2.45 15.24 30.13 0.1 45.57 44.47

(2.591, 2.1) 0.25 13.7 2.45 2.84 14.35 0.2 17.45 17.28

(2.610, 3.5) 0.27 14.4 2.45 2.61 7.07 0.2 9.95 10.03

(2.623, 5.0) 0.27 14.4 2.45 2.67 3.94 4.0 6.88 6.91

(2.632, 6.5) 0.28 14.4 2.45 2.42 2.51 7.9 5.21 5.34

(2.675, 22.7) 0.28 14.4 2.45 0.58 0.72 15.8 1.58 1.57

(2.691, 35.8) 0.28 17.0 2.45 0.42 0.33 28.9 1.02 1.00

TABLE IIIPARAMETERS FITTED FOR THE RED LED

Bias(V, mA) Rb(Ω) Cb(nF) Lb(nH) Rs(Ω) rd(Ω) Cj (nF) Rsum(Ω) nkT/qI0 +RsDC (Ω)

(0.000, 0) 1.78 0.29 0.99 − − − − −

(1.500, 0) 1.60 0.23 0.99 7.60 4113.59 0.45 4122.79 1900.23

(1.595, 0.5) 1.65 0.25 0.99 6.63 350.14 1.12 358.42 188.91

(1.662, 1.2) 1.66 0.27 0.99 4.06 43.48 4.72 49.20 37.33

(1.694, 2.4) 1.58 0.27 0.99 2.56 14.32 10.9 18.47 17.34

(1.715, 4.0) 1.58 0.27 0.99 1.92 7.50 18.1 11.01 10.55

(1.730, 5.8) 1.21 0.19 0.99 1.96 4.89 24.7 8.06 7.43

(1.770, 15.0) 1.21 0.19 0.99 1.28 1.46 49.7 3.95 3.03

(1.794, 24.7) 1.38 0.19 0.99 0.78 0.83 75.1 2.99 1.85

(1.813, 35.2) 1.47 0.19 0.99 0.54 0.53 100 2.54 1.30

(1.829, 45.7) 1.35 0.19 0.99 0.54 0.39 130 2.28 1.00

C. S21 Measurement

For the S21 measurement, a higher AC input current wasuesd to drive the LED in order to provide a sufficient opticalpower at the optical receiver. The AC power was increasedaccordingly for different bias conditions while keeping themeasured impedance curves the same as what was measuredwith −40 dBm output power to ensure nonlinearity does notoccur and the corresponding impedance models match.

Figs. 8 and 9 show the measured and estimated normalizedS21 of the white and red LEDs. The estimated model showsa strong correlation with the red LED, however, the whiteLED response does not agree well with the model due to theeffect of the phosphor coating [21] at low frequencies andinaccuracy of the impedance fitting at high frequencies. The

second knee points followed by a −60 dB/dec slope causedby parasitic elements are predicted by the model and agreewell with measured S21 parameter for the red LED. It hasalso been observed that the knee points for the white LED arehighly correlated with the anti-resonance peaks.

IV. CONCLUSION

The effective impedance measurement using the one-portreflection method was adopted to model the entire high powerLED chip. The equivalent circuit model not only unveiled theimpedance characteristics of those high power LEDs, but alsoprovided an accurate way to estimate the frequency responsein the optical domain. Extensive experiments were carried outto confirm the accuracy of this technique.

104 105 106 107 108 109 1010

Freq(Hz)

10-1

100

101

102

103

104

Mag

(Z)(

Ohm

)(0.0 V, 0.000 V, 0 mA)(1.0 V, 1.000 V, 0 mA)(2.0 V, 2.000 V, 0 mA)(2.1 V, 2.100 V, 0 mA)(2.2 V, 2.200 V, 0 mA)(2.3 V, 2.300 V, 0 mA)(2.4 V, 2.400 V, 0 mA)(2.5 V, 2.493 V, 0.2 mA)(2.6 V, 2.558 V, 0.8 mA)(2.7 V, 2.591 V, 2.1 mA)(2.8 V, 2.610 V, 3.5 mA)(2.9 V, 2.623 V, 5.0 mA)(3.0 V, 2.632 V, 6.5 mA)(4.0 V, 2.675 V, 22.7 mA)(5.0 V, 2.691 V, 35.8 mA)

Fig. 5. Measured impedance of the white LED

104 105 106 107 108 109 1010

Freq(Hz)

100

101

102

103

104

105

Mag

(Z)(

Ohm

)

(0.0 V, 0.000 V, 0.0 mA)(1.5 V, 1.500 V, 0.0 mA)(1.6 V, 1.595 V, 0.5 mA)(1.7 V, 1.662 V, 1.2 mA)(1.8 V, 1.694 V, 2.4 mA)(1.9 V, 1.715 V, 4.0 mA)(2.0 V, 1.730 V, 5.8 mA)(2.5 V, 1.770 V, 15.0 mA)(3.0 V, 1.794 V, 24.7 mA)(3.5 V, 1.813 V, 35.2 mA)(4.0 V, 1.829 V, 45.7 mA)

Fig. 6. Measured impedance of the red LED

V. ACKNOWLEDGMENT

This work is supported by the European Unions Horizon2020 research and innovation programme under the MarieSlodowska-Curie grant agreement no 764461 (VISION), theUK EPSRC research grant EP/P006280/1: MARVEL and theCzech Science Foundation project GACR 17-17538S.

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104 105 106 107 108 109

Freq(Hz)

10-1

100

101

102

Ma

g(Z

)(O

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-100

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104 105 106 107 108 109 1010

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Fig. 9. Measured and fitted impedance of the red LED biased at 5.8mA,45.7mA

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